I just saw this item posted on a Homebrew product blog. They noted that the humidity has no value but I thought it would be perfect for a cave. Cool part is it does daily high/low recording for both temp and humidity. It's also has magnetic backing.
Right now $8.94 with free shipping over $25 or Prime members.
AcuRite 00325 Home Comfort Monitor, Black by Acu-Rite
Here is one of the user images that did some simple testing on accuracy.